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Math Help - Bionomial & Approximation Distribution - Probability

  1. #1
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    Bionomial & Approximation Distribution - Probability

    What is the probability of getting exactly 40 heads if a fair coin is tossed 50 times, using:

    a) The binomial distribution formula?
    b) The normal approximation to the binomial distribution?

    MY ANSWERS:

    a) p(x) = c(n,x) p^x q ^n-x
    p(x=40) = c(50,40) (4/5)^40 (4/5)^10

    Now would that be correct??? I do that and I get a ridiculous number.

    b) SD(standard deviation)= Squareroot(SR) of =npq
    Sd=SR 50x0.8x0.2
    SD= SR = 8
    SD= 2.83

    z = 39.5 - 50/2.83 = -10.5/2.83 = -3.71

    Using the z-score table 0.4999 = 49.9% of getting exactly 40 heads.

    Something seems off, can someone direct me to where I am going wrong?
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  2. #2
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    Re: Bionomial & Approximation Distribution - Probability

    p, the probability of the coin coming down heads, is 1/2 not 4/5.
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  3. #3
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    Re: Bionomial & Approximation Distribution - Probability

    So other then that, I am on the correct track??
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  4. #4
    MHF Contributor matheagle's Avatar
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    Re: Bionomial & Approximation Distribution - Probability

    exact prob is

    {50\choose 40}(.5)^{50}

    normal approximation is

    P(39.5<X<40.5)=P\left({39.5-\mu\over \sigma}<Z<{40.5-\mu\over \sigma}\right)

    where

    \mu= np=50(.5) and  \sigma^2=npq=50(.25)
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